{"paper":{"title":"Non-tracial free graph von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Brent Nelson, Michael Hartglass","submitted_at":"2018-10-03T19:21:07Z","abstract_excerpt":"Given a finite, directed, connected graph $\\Gamma$ equipped with a weighting $\\mu$ on its edges, we provide a construction of a von Neumann algebra equipped with a faithful, normal, positive linear functional $(\\mathcal{M}(\\Gamma,\\mu),\\varphi)$. When the weighting $\\mu$ is instead on the vertices of $\\Gamma$, the first author showed the isomorphism class of $(\\mathcal{M}(\\Gamma,\\mu),\\varphi)$ depends only on the data $(\\Gamma,\\mu)$ and is an interpolated free group factor equipped with a scaling of its unique trace (possibly direct sum copies of $\\mathbb{C}$). Moreover, the free dimension of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01922","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}